Answer:
Rhombus
Step-by-step explanation:
Apply the formula for finding distance using coordinates to find the length of the sides of the parallelogram
Given the coordinates as;
P(6,-6) , Q(1,1),R(-6,6),S(-1,-1)
Finding the lengths
The formula to apply is;
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
For PQ where you have : P(6,-6) , Q(1,1)
[tex]d=\sqrt{(1-6)^2+(1--6)^2}\\\\d=\sqrt{(-5)^2+(7)^2} \\\\d=\sqrt{25+49} \\\\d=\sqrt{74} \\\\d=8.60[/tex]
You can also apply the Pythagorean relationship to get the leg distance and calculate the hypotenuse .For example to get the length of QR ;
QR² = 7²+5²
QR = √49+25
QR = 8.60
You notice all sides are equal , 8.60 units
You also notice the opposite angles are equal
This is a rhombus
